ebcov {saeeb}

EB Poisson-Gamma with Covariates

Description

This function gives the area level EB and MSE estimator based on Wakefield (2006) model and the refinement model by Kismiantini (2007).

Usage

ebcov(formula, data, e)

Arguments

formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.

data

a mandatory data frame containing the variables in formula and e.

e

a variable that contains the expected numbers of cases in each area.

Details

A typical model has the form response ~ terms where the response is a vector with numeric data type and terms is a set(s) of auxiliary variables.

A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x. See formula for more details of allowed formulae.

The formula only accomodates variables with count data type and will be modeled using binomial negatif linear regression.

Value

The function returns a list with the following objects:

EB

data frame with number of rows equal to number of areas containing the EB estimator. For domains with zero sample size, the EB estimators are based on the synthetic regression.

Parameter

• alpha: the scale parameter estimator in Gamma distribution

• v: the shape parameter estimator in Gamma distribution

fit

• Estimate: maximum likelihood estimator of the model parameters

• SE: asymptotic estimate of the standard error of the the parameters

• Z: the Z statistic of the asymptotic hypothesis test that the population value for the parameter is 0

• LCL: lower 95% confidence interval for the parameter estimators

• UCL: upper 95% confidence interval for the parameter estimators

MSE.EB

• method: Jackknife

• mse: the mean squared error estimator of the EB estimators

direct

• est: direct estimators for the response variable

• mse: the mean squared error estimator of the direct estimators

See Also

ml.nb2, glm.nb,

Examples

#Load dataset
data(lip)

#Save output as an object
results <- ebcov(Y ~ AFF, lip, E)
results